Summer 2023 A WEIGHTED COMPACTNESS CRITERION FOR COMMUTATORS ASSOCIATED WITH GENERALIZED CALDERÓN–ZYGMUND OPERATORS
Li Yang, Qianjun He, Pengtao Li, Kai Zhao
J. Integral Equations Applications 35(2): 235-257 (Summer 2023). DOI: 10.1216/jie.2023.35.235

Abstract

Let T be a bounded operator on Lp(n). Under the assumption that the kernel of T satisfies some Hörmander-type estimates, we obtain a boundedness criterion for the multilinear commutators Tb on the weighted Lebesgue spaces Lp(ω) with bBMO(n) and ω belonging to the Muckenhoupt weight class Apm. Further, for bCMO(n), the vanishing mean oscillation space, a criterion of Lp-weighted compactness of Tb is established. As applications, the weighted Lp-boundedness and Lp-compactness criteria can be applied to the 𝜃-type Calderón–Zygmund operator and its commutators.

Citation

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Li Yang. Qianjun He. Pengtao Li. Kai Zhao. "A WEIGHTED COMPACTNESS CRITERION FOR COMMUTATORS ASSOCIATED WITH GENERALIZED CALDERÓN–ZYGMUND OPERATORS." J. Integral Equations Applications 35 (2) 235 - 257, Summer 2023. https://doi.org/10.1216/jie.2023.35.235

Information

Received: 28 January 2023; Revised: 3 May 2023; Accepted: 4 May 2023; Published: Summer 2023
First available in Project Euclid: 25 October 2023

Digital Object Identifier: 10.1216/jie.2023.35.235

Subjects:
Primary: 22E30
Secondary: 35J10 , 42B35 , 47B38

Keywords: commutator , compactness , ‎weight function

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.35 • No. 2 • Summer 2023
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